Assume now that we have a toroidal embedding of Artin stacks \((\mathcal {U}\subset \mathcal {X})\) , locally of finite type over \(k\) . Associated to \((\mathcal {U}\subset \mathcal {X})\)  there is a canonical topological space \(\Sigma (\mathcal {X})\) , together with a canonical compactification \(\overline{\Sigma }(\mathcal {X})\) , and a functorial analytic tropicalization map \(\operatorname{trop}_{\mathcal {X}}^{an}:|\mathcal {X}^{\beth }|\rightarrow \overline{\Sigma }(\mathcal {X})\) , that we are now going to review following [1]} (which deals with the more general situation of logarithmic Artin stacks) and [2]} (which deals with the special case of toroidal embeddings of DM-stacks).
